One of the advantages of \(ME\)  over \(FBA\)  is that its solution is a full probabilistic description of the metabolic state of the culture.
Figure (REF ) shows the marginal distributions for the free fluxes at different values of \(\epsilon \)  for simulations at a fixed \(D\) .
The upper row shows the distributions produced by the dynamical simulation and the lower row the ones inferred using \(ME\) .
As we already showed before, \(ME\)  infers correctly the mean values (dotted lines) of the distribution, but although we can see that it also describes quite well the real shape of the distributions, there are differences.
This gives us an important insight: even if we encode correctly the constraints that are defining \(\mathbb {V}\)  and \(\bar{\mathbb {V}}\) , and if these definitions really describe the boundary of the experiments (the simulations), our \(ME\)  formulation does not include information about constraints acting over higher order moments of the distributions.
In this particular case, the arbitrary \(\mathcal {P}\)  transformation introduced on the dynamic for enforcing the moment constraints, although not affecting \(\mathbb {V}\)  or \(\bar{\mathbb {V}}\) , is generating a non-uniform effect that differentiate the distribution computed directly from the simulations from the one inferred through \(ME\) , \(\mathcal {P_{ME}}\) .
If those extra constraints were encoded in the model, \(ME\)  is expected to recover the distributions completely [1]}.
